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Nash Equilibrium In Game Theory ~xRay Pixy

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 Video Link  CLICK HERE... Learn Nash Equilibrium In Game Theory Step-By-Step Using Examples. Video Chapters: Nash Equilibrium  00:00 Introduction 00:19 Topics Covered 00:33 Nash Equilibrium  01:55 Example 1  02:30 Example 2 04:46 Game Core Elements 06:41 Types of Game Strategies 06:55  Prisoner’s Dilemma  07:17  Prisoner’s Dilemma Example 3 09:16 Dominated Strategy  10:56 Applications 11:34 Conclusion The Nash Equilibrium is a concept in game theory that describes a situation where no player can benefit by changing their strategy while the other players keep their strategies unchanged.  No player can increase their payoff by changing their choice alone while others keep theirs the same. Example : If Chrysler, Ford, and GM each choose their production levels so that no company can make more money by changing their choice, it’s a Nash Equilibrium Prisoner’s Dilemma : Two criminals are arrested and interrogated separately. Each has two ...
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Ant Colony Optimization Numerical Example Step-By-Step ~xRay Pixy

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Ant Colony Optimization Numerical Example Step-By-Step
00:00 Introduction
01:34 Ant Colony Optimization Steps
04:33 Step 1 Parameter Initialization
06:14 Step 2 Population Initialization
06:40 Step 3 Path Selection by Ants
12:16 Step 4 Objective Function Evaluation
14:28 Step 5 Test Convergence
15:27 Step 6 Second Iteration Start
15:36 Step 7 Pheromone Update
18:20 Step 8 Repeat ACO Loop
19:27 Path Selection by Ants
21:42 Objective Function Evaluation
22:51 Test Convergence
22:58 Third Iteration
23:25 Pheromone Update
24:26 Path Selection by Ants
25:00 Conclusion

Ant Colony Optimization (ACO) Algorithm Steps

  1. Initialize Parameters.
  2. Initialize Ants Population.
  3. Calculate Path Selection Probability by ants.
  4. Apply Roulette Wheel Selection Process.
  5. Calculate Objective Function Values.
  6. Test Process Convergence.
  7. Increment Counter.
  8. Update Pheromones.
  9. Repeat Step 3 to Step 6.
  10. Display Best Solution 
How to Calculate Path Selection Probability by Ants?
For any ant (k), the Probability of Selecting a Path / Discrete Value is Calculated as: 

How to Update Pheromones?
 Remaining pheromones from the previous iteration after evaporation

Pheromone Deposited by Best Ant.


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